fdm {demography}

Functional demographic model

Description

Fits a basis function model to demographic data. The function uses optimal orthonormal basis functions obtained from a principal components decomposition.

Usage

fdm(
  data,
  series = names(data$rate)[1],
  order = 6,
  ages = data$age,
  max.age = max(ages),
  method = c("classical", "M", "rapca"),
  lambda = 3,
  mean = TRUE,
  level = FALSE,
  transform = TRUE,
  ...
)

Arguments

data

demogdata object. Output from read.demogdata.

series

name of series within data holding rates (1x1).

order

Number of basis functions to fit.

ages

Ages to include in fit.

max.age

Maximum age to fit. Ages beyond this are collapsed into the upper age group.

method

Method to use for principal components decomposition. Possibilities are “M”, “rapca” and “classical”. See ftsm for details.

lambda

Tuning parameter for robustness when method="M".

mean

If TRUE, will estimate mean term in the model before computing basis terms. If FALSE, the mean term is assumed to be zero.

level

If TRUE, will include an additional (intercept) term that depends on the year but not on ages.

transform

If TRUE, the data are transformed with a Box-Cox transformation before the model is fitted.

...

Extra arguments passed to ftsm.

Value

Object of class “fdm” with the following components:

label

Name of country

age

Ages from data object.

year

Years from data object.

<series>

Matrix of demographic data as contained in data. It takes the name given by the series argument.

fitted

Matrix of fitted values.

residuals

Residuals (difference between observed and fitted).

basis

Matrix of basis functions evaluated at each age level (one column for each basis function). The first column is the fitted mean.

coeffs

Matrix of coefficients (one column for each coefficient series). The first column are all ones.

mean.se

Standard errors for the estimated mean function.

varprop

Proportion of variation explained by each basis function.

weights

Weight associated with each time period.

v

Measure of variation for each time period.

type

Data type (mortality, fertility, etc.)

y

The data stored as a functional time series object.

Author(s)

Rob J Hyndman

References

Hyndman, R.J., and Ullah, S. (2007) Robust forecasting of mortality and fertility rates: a functional data approach. Computational Statistics & Data Analysis, 51, 4942-4956. https://robjhyndman.com/publications/funcfor/

See Also

ftsm, forecast.fdm

Examples

france.fit <- fdm(fr.mort)
summary(france.fit)
plot(france.fit)
plot(residuals(france.fit))